Remark on factorials that are products of factorials

In a paper published in 1993, Erdos proved that if n! = a! b!, where 1 < a a parts per thousand currency sign b, then the difference between n and b does not exceed 5 log log n for large enough n. In the present paper, we improve this upper bound to ((1 + epsilon)/ log 2) log log n and generalize it to the equation a (1)!a (2)! ... a (k) ! = n!. In a recent paper, F. Luca proved that n - b = 1 for large enough n provided that the ABC-hypothesis holds.

Analysis of co-current hydraircooling of food products in bulk

A mathematical model is developed to describe the hydraircooling process when the water and air are flowing in the same direction. The governing equations for the simultaneous heat and mass transfer are solved using finite-difference numerical methods. The half cooling time of the food products is correlated as a function of the dimensionless process parameters. It is observed that a process time of approximately double the half cooling time will result in the food products attaining almost a steady state. The process times of the bulk hydraircooling process and the bulk air precooling process are compared.

Dynamic response of latex modified concrete machine foundations

New materials in concrete constructions have been widely used to improve various properties such as impact resistance, strength and durability. Polymer modified concrete is one of the new materials which has been developed for potential application in the construction industry. This Paper describes the use of polymer latex for foundation blocks subjected to dynamic loads. Experiments were conducted using ordinary concrete and latex modified concrete footings of three different thicknesses, for three static loads at four excitation levels. Experimental results have revealed that the amplitude of resonance is reduced considerably in the latex modified concrete footings.

Analysis of heat and mass transfer during bulk hydraircooling of spherical food products

Hydraircooling is a technique used for precooling food products. In this technique chilled water is sprayed over the food products while cold unsaturated air is blown over them. Hydraircooling combines the advantages of both air- and hydrocooling. The present study is concerned with the analysis of bulk hydraircooling as it occurs in a package filled with several layers of spherical food products with chilled water sprayed from the top and cold unsaturated air blown from the bottom. A mathematical model is developed to describe the hydrodynamics and simultaneous heat and mass transfer occurring inside the package. The non-dimensional governing equations are solved using the finite difference numerical methods. The results are presented in the form of time-temperature charts. A correlation is obtained to calculate the process time in terms of the process parameters.

Chiral polyhydroxylated tetrahydrothiophene derivatives: novel synthesis and structural elucidation by X-ray crystallography, NMR spectroscopy and molecular mechanics calculations

The dideoxygenation reaction of 1,3;4,6-di-O-alkylidene-2,5-di-S-methylthiocarbonyl-D-mannitol derivatives under Barton-McCombie reaction conditions gave the hexahydrodipyranothiophenes 4 and 7 instead of the expected 2,5-dideoxy products. Structural and conformational information on these novel derivatives has been obtained by NMR spectroscopy, single-crystal X-ray crystallography and molecular mechanics calculations.

Do the Hydrolysis Products, Methylamine and N,N'-Dimethylurea, Play any Role in the Methyl Isocyanate-Induced Haematological and Biochemical Changes in Rabbits?

The subcutaneous administration of methyl isocyanate (MIC) to female rabbits, resulted in significant increases in haemoglobin concentration, erythrocyte volume fraction and leucocyte number in blood, as well as plasma total proteins, and urea. The present study was designed to investigate whether the hydrolytic products of MIC, methylamine (MA) and N,N'-dimethylurea (DMU) play any role in eliciting these changes. Both MA and DMU administered subcutaneously in an equimolar dose to that of 1.0 LD50 MIC, 2.2 mmol kg-1, had no influence on these parameters, although there was a marginal increase in the plasma urea level shortly after the administration of DMU. This study establishes that the observed haematological and biochemical changes induced by MIC intoxication in rabbits are mostly due to MIC.

Influence of methylamine and N,N'-dimethylurea, the hydrolysis products of methyl isocyanate, on its systemic toxicity

Subcutaneous administration of the LD50 dose of methyl isocyanate (MIC) to rats induced severe hyperglycaemia, lactic acidosis and uraemia in rats. Neither methylamine (MA) nor N,N′-dimethylurea (DMU), the hydrolysis products of MIC, administered in equimolar doses had any influence on these parameters except for a marginal transient increase in plasma urea by DMU. Methyl isocyanate administration led to haemoconcentration, resulting in an increase in the plasma concentration of total proteins and a decrease in both the plasma concentration of albumin and the plasma cholinesterase activity. The hydrolysis products of MIC had no influence on any of these parameters. Thus, it seems reasonable to suggest that the systemic effects of MIC are caused by MIC per se, in spite of its high hydrolytic instability.

Potassamide induced in situ alkylation of 5,6-dihydroisoquinolines: Structure of products

Potassamide induced in situ alkylation of 1-alkyl- 4-cyano-3-methoxy-5,6-dihydroisoquinolines (2a & 2b) with alkyl iodides (CH3I, CH3CH2I & cyclohexyl iodide) gave the 5-alkyl- and 5,9-dialkyl-5,6-dihydroisoquinolines (4–ad & 3a–e), isoquinoline derivatives, (5a–b) and diastereomeric mixture of 4- alkyl-1,2,3,4-tetrahydroisoquinolin-3(2H)-ones (6a–e & 6′a–e). Structures were assigned on the basis of spectral data [Mass, 1H & 13C NMR, 2D NOESY & HC-COLOC]. Amide induced in situ alkylation of compounds 3a and 4a with CH3I gave in almost quantitative yield the dimethylated compounds 3d and 3a respectively. While KNH2/liq.NH3 methylation of 1,2- dihydroisoquinoline, 1 with CH3I gave the mixture of compounds, 6a & 6′a and the isoquinoline derivative 5a, NaH/benzene reaction of 1 with CH3I gave exclusively 5a. N-methylation of the mixture of compounds 6a & 6′a with NaH/CH3I gave the methylated derivatives, 7 & 8. A suitable mechanism has been proposed for the formation of products.

Reaction of spironaphthalenones with hydroxylamine: Part III. A novel mechanism for the formation of products and trapping of an intermediate.

A mechanism involving the intermediacy of nitrene 5, formed from the oxime of spironaphthalenone 1 by acid catalysed dehydration, has been proposed to explain the formation of pyrrolotropones/pyrrolo esters from spironaphthalenones. The initially formed nitrene rearranges to the isopyrrole 6, which either undergoes sigmatropic migration to the pyrrolotropone 2 or adds alcohol to form the pyrrolo ester depending on substitution at 1′ position. The isopyrrole intermediate 6 has been trapped as a Diels-Alder adduct 8.

Porous, catalytically active palladium nanostructures by tuning nanoparticle interactions in an organic medium

We present a simple template-free method for the synthesis of interconnected hierarchical porous palladium nanostructures by controlling the aggregation of nanoparticles in organic media. The interaction between the nanoparticles is tuned by varying the dielectric constant of the medium consistent with DLVO calculations. The reaction products range from discrete nanoparticles to compact porous clusters with large specific surface areas. The nanoclusters exhibit hierarchical porosity and are found to exhibit excellent activity towards the reduction of 4-nitrophenol into 4-aminophenol and hydrogen oxidation. The method opens up possibilities for synthesizing porous clusters of other functional inorganics in organic media.

Excision of uracil from the ends of double stranded DNA by uracil DNA glycosylase and its use in high efficiency cloning of PCR products

We show that uracil DNA glycosylase from E. coli excises uracil residues from the ends of double stranded oligos. This information has allowed us to develop an efficient method of cloning PCR amplified DNA. In this report, we describe use of this method in cloning of E. coli genes for lysyl- and methionyl-tRNA synthetases. Efficiency of cloning by this method was found to be the same as that of subcloning of DNA restriction fragments from one vector to the other vector. Possibilities of using other DNA glycosylases for such applications are discussed.

Potassamide induced in situ benzylation of 5,6-dihydroisoquinolines: Structure of novel products

Potassamide induced in situ benzylation of 1-alkyl-4-cyano-3-methoxy-5,6-dihydroisoquinolines (1a-b) with benzyl iodide gave the 5-benzyl-, 5,9-dibenzyl- and 4,4-dibenzyl-5,6-dihydroisoquinolines (9a-b, 8a-b and 10a-b), isoquinoline derivatives (4a-b) and diastereomeric mixture of 4-benzyl-1,2,3,4-tetrahydroisoquinolin-3(2H)-ones (11a-b & 11'a-b). Structures were assigned on the basis of spectral data [Mass, H-1 & C-13 NMR, 2D NOESY]. A few reactions carried out to transform the diastereomeric mixture of compounds 11a and 11's to the spirobenzylisoquinoline system 7a isomeric with naturally occurring ochotensane system ga are discussed.

Thermal degradation products of poly(styrenesulfides) investigated by direct pyrolysis�mass spectrometry and flash pyrolysis�gas chromatography/mass spectrometry

The thermal degradation products of two sulfur polymers, poly(styrenedisulfide) (PSD) and poly(styrenetetrasulfide) (PST), were investigated in parallel by direct pyrolysis-mass spectrometry (DPMS) and by flash pyrolysis-GC/MS (Py-GC/MS). The time-scale of the two pyrolysis techniques is quite different, and therefore they were able to detect significantly different products in the pyrolysis of PSD and PST because of the thermal lability of sulfur-containing compounds. However, the results obtained are not contradictory, and satisfactory mechanisms for the thermal degradation of PSD and PST have been derived from the overall evidence available. Pyrolysis compounds containing sulfur, styrene, and a number of cyclic styrene sulfides and diphenyldithianes have been observed by DPMS. However, in flash pyrolysis-GC/MS, styrene, sulfur, only one cyclic styrene sulfide, and two isomers of diphenylthiophene have been detected. These thiophene derivatives were indeed absent among the compounds obtained by DPMS because they were the terminal (most thermally stable) species arising from further decomposition of the cyclic styrene sulfides formed in the primary thermal degradation processes of PSD and PST.